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Refined functional equations stemming from cubic, quadratic and additive mappings

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Abstract

Let n ≥ 2 be an integer. In this paper, we investigate the generalized Hyers-Ulam stability problem for the following functional equation

$$ f\left( {\sum\limits_{j = 1}^{n - 1} {x_j + 2x_n } } \right) + f\left( {\sum\limits_{j = 1}^{n - 1} {x_j - 2x_n } } \right) + 8\sum\limits_{j = 1}^{n - 1} {f\left( {x_j } \right) = 2f\left( {\sum\limits_{j = 1}^{n - 1} {x_j } } \right)} + 4\sum\limits_{j = 1}^{n - 1} {\left[ {f\left( {x_j + x_n } \right) + f\left( {x_j - x_n } \right)} \right]} $$

, which contains as solutions cubic, quadratic or additive mappings.

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Authors and Affiliations

  1. Department of Mathematics, Mokwon University, Seo-Gu, Daejeon, 302-729, Republic of Korea

    Ick-Soon Chang

  2. Department of Mathematics, Chungnam National University, 220 Yuseong-Gu, Daejeon, 305-764, Republic of Korea

    Eunyoung Son & Hark-Mahn Kim

Authors
  1. Ick-Soon Chang
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  2. Eunyoung Son
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  3. Hark-Mahn Kim
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Correspondence to Hark-Mahn Kim.

Additional information

This study was financially supported by research fund of Chungnam National University in 2008

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Chang, IS., Son, E. & Kim, HM. Refined functional equations stemming from cubic, quadratic and additive mappings. Acta. Math. Sin.-English Ser. 25, 1595–1608 (2009). https://doi.org/10.1007/s10114-009-7190-z

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  • DOI: https://doi.org/10.1007/s10114-009-7190-z

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